Critical Note on the Surface Resistance Coefficient in the Atmospheric Flow over the Ocean

Critical Note on the Surface Resistance

Coefficient in the Atmospheric Flow over the

Ocean

著者

TAKAHASHI Tadao

雑誌名

鹿児島大学水産学部紀要=Memoirs of Faculty of

Fisheries Kagoshima University

巻

4

ページ

65-70

CriticalNoteontheSurfaceResistanceCoefficient intheAtmospheriｃＦＩｏｗｏｖｅｒｔｈｅＯｃｅａｎ ＴａｄａｏＴＡＫＡＨＡｓＨＩ 6５ １．Introduction ｌｔｉｓａｗｅｌｌｋｎｏｗｎｆａｃｔｔｈａｔｔｈｅｗｉｎｄｏvertheseaiscomparativelystron‐ gerthanoverland，ａｓｅｘｐｌａｉｎｅｄｂｙｔｈｅｓｍａｌｌｎｅｓｓｏｆｔｈｅfrictionaldragover thesea・MoreoverthisfacthasafamiliarsynOpticsignificancethattheincli-nationangle（α）ｏｆｔｈｅｗｉｎｄｔｏｔｈｅｉｓｏｂａｒｓｏｖｅｒｔｈｅｓｅaissmallerthanthat overland、 AssumingF＝一kVforthefrictionalforce（ｋ，coefficientoffriction；Ｖ，

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（ｆ＝2のsinや：Coriolisparameter）underthebalancedthreeforces，ｉ､e･pressure gradient，deflecting，andfrictional・Takingtheinferredvalueofk＝0.00002ｏｖｅｒ ｔｈｅｓｅａａｎｄｔｈａｔｏｆｋ＝0.00012ｏｖｅｒland，theyderivedthesynopticallyreason-ablevalueofα＝10o58’ａｎｄα＝49ol9ノrespectively（ａｔリー45｡）．Howeverthis simpleassumptionwasbesidesthemarkandanewtreatmentbyeddytheory hadtobeintroduced・

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eddydiffusivityassumedtobeconstantinthefrictionallayer，ａｎｄｌ０ｉｓｄｅｎｓｉ− ｔｙｏｆａｉｒ・Slippingvelocity（Ｖｂ）ｕｐｏｎｔｈｅｇｒｏｕｎｄｏｒｓｅａｓｕｒｆａｃｅｉｓｃｏｎnected withthesurfacestress（で｡）ｂｙ､theequationで｡＝に,０Ｖ:，where施ｉｓｔｈｅｃｏｅｆ‐

………．i伽c…k…mUSing娠=2KB等､"(B三竺署聖加

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Ｚ＝Ｏ ｔｈｅｖａｌｕｅｏｆ応fromDobsonﾉspilotballoonObservationsoverSalisburyPlane， andobtainedに＝0.0023,0.0032,0.0022ｆｏｒlight，moderate，andstrongwind respectively．

Ｄ･Brunt(3)proposedthemostprobablevalueofにｔｏｂｅ0.004fromStantonFs

experimentofpiｐｅｆｌｏｗ・HenoticedthatTaylorﾉｓｖａｌｕｅｏｆにdidnotshow systematicvariationwithwindspeed，ａｎｄｔｈａｔｔｈｅｖａｌｕｅｓｏｆ苑werecomparable intheabove-mentiｏｎｅｄｔｗｏｃａｓｅｓｉｎｓｐｉｔｅｏｆｔｈｅｒａｔｉｏｏftheReynold『ｓｎｕｍｂ‐ erswhichwasmorethanlO5･Ａｎｄｈｅｓｔａｔｅｄｔｈａｔｔｈｅｓａｍｅｌａｗａｐｐｅａredto holdoververywiderange・Sincethen，theideathatthecoefficientofskin frictionisindependentofsurfacestateshasbeenprevailedimplicitelyamong meteorologists・ However，thisassumptionofindependencyisverydoubtful・Ｗｅｃａｎｓｈｏｗ

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andisabouttwo-thirdoverthesea"，isgenerallyacceptable・Ａｎｄｗｅｈａｖｅ

6６ _{Ｍｅｍ・Fac・Ｆｉｓｈ・ＫａｇｏｓｈｉｍａＵｎｉｖ・vol、４，} α＝32．ｆｏｒｌａｎｄａｎｄα＝17．ｆｏｒｔｈｅｓｅａ，byusingthewellknownTaylorﾉs

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ｗｅｇｅｔＫ＝１．７×105ｆｏｒｔｈｅｓｅａａｎｄＫ＝３．４×１０３ｆｏｒｌａｎｄ（ａｔ？＝４５ｏａｎｄｗｈｅｎ Ｇ＝１０ｍ/seｃ）．Thisconclusion，ｗｈｉｃｈｓｈｏｗｓｔｈａｔｔｈｅｖａｌｕｅｏｆｅｄｄｙｄｉffusivity overtheseaishigherthanoverland，isobviouslycontradictorytothefact． ２．DeterminationofcoefficientofsurfaceresistancefromPilotbalIoon observations Amethodoftheestimationof花frompilotballoonobservationsdevised

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internalfrictionareinequilibrium，x-componentequationofmotionincartesian

…in…fv-÷袈十÷詩=0,W伽Ⅷ‘……n'ofwind

velocity，でxisx-componentofshearingstress，andppressure・Bysubstituting they-componentofthegeostrophicwind（Ｇｙ）forthebarometricgradient

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levelatwhichGy＝ｖｏｒでｘ（ｈ）＝Oistobesatisfied・ Theprominentmeritofthismethodisthatitinvolvesnoassumptionas tothewinddistributionalongthevertical,whileTaylorﾉsmethodinvolvesthe assumptionoftheconstancyofKinthefrictionallayer･AdOptingthismethod tokiteObservationsmadeonboardtheGermanresearchvessel〃Meteor〃over

theNorthandSouthAtlantic，Sutcliffefound随＝４×10-4（ｍｅａｎvalue)、Ｂｕｔ

ｔｈｉｓｌｏｗｖａｌｕｅｏｆ左ｏｖｅｒｔｈｅｏｃｅａｎｗａｓｎｏｔａｃｃｅｐｔｅｄｂｙｓｏmemeteorologists

whoanticipatedtheindependencyof施fromsurfacestates・ JForapreliminaryresearchofthegeneralcirculationoftheatmosphere sometrialstodetermineareasonablevalueofthecoefficientofskinfriction

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performeddetailedpilotballoonobservationsovertheseainthewesterlies・ Butthedeterminationof施bySutcliffeﾉsmethodfailedbecauseoftheirmis‐ singalevelwhererx（ｚ）vanished・

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gotfromtheobservatioｎａｌｄａｔａａｔｖｅｒｙｓｍａｌｌｉｓｌａｎｄｓｉｎｔｈｉｓｂｅｌｔａｒｅｌｉｓｔｅｄｉｎ Ｔａｂｌｅｌ・WiththeexceptionofthevaluesforSanJuanlsland，ｔheorderofthe

obtainedvaluesof応indicateslO×１０−４，andwithouthavinganysystematic

variationwiththewindspeed．（Theinducementoftheexceptionalhigher

１ １ 〃 1 ０ 〃 1 １ 〃 ６ 〃 6７ Eniwetok Takahashi：Ｓｕｒｆａｃｅｒｅｓｉｓｔａｎｃｅｉｎｆｌｏｗｏｖｅｒｔｈｅocean valuesforSanJuanIslandisattributedbytheauthorstotheorographic effects，ｗｈｉｌｅｉｎＣ.Ｈ､Ｂ・Priestlyﾉｓｓｕｇｇｅｓｔｉｏｎｉｔｉｓｉｍｐｕｔｅｄｔｏｔｈｏｓｅｏfthe verticalvelocity.） Ｓｏｆａｒ，ｔｈｅｖａｌｕｅｏｆだ＝１０×10-4isplausible，ｔｈａｔｉｓｔｈｅｓｍａｌｌｎｅｓｓｏｆにｏｖｅｒ ｔｈｅｏｃｅａｎｉｓａｓｓｕｒｅｄｔｏｂｅａｆａｃｔ・ Ｔａｂｌｅｌ ３．DeterminationofcoefficientofsurfacereSistancefromthevelOciｔｙ ｐｍｆｉｌｅｓｉｎｔｈｅｓｋｉｎｌａｙｅｒ

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edhere・AssumingthevelocityprofileintheskinlayerobeysPrandtlﾉｓ

ｆ…,a｡Ⅳ=古I/〒1,等竺,wh…｡い｡nK…,ScⅧ…

0.38,zoroughnessparameter，ａｎｄでisshearingstresswhichisconstant throughouttheskinlayer,andeliminatingでfromtherelationで＝即Ｖ２，ｔｈｅｙｇｅｔ ｋ ：

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atwhichsynopticalsurfacewindismeasured・Theyobtainedだ＝１９×１０−４with zo＝0.5ｃｍｄｅｄｕｃｅｄｂｙｔｈｅｍｆｒｏｍＨｅｌｌｍａｎ「ｓｄａｔａｏｖｅｒｔｈｅｌａｗｎａｔＮａｕｅｎ， andだ＝３１×１０−４ｗｉｔｈｚＯ＝３．２ｃｍｆｒｏｍＳｈａｗﾉsdataoveropengrassland・ SimilanytheyanalysedtheWiistrsobservationsoftｈｅｗｉｎｄｏｖｅｒｔｈｅ ＢａｌｔｉｃＳｅａｗｉｔｈｔｈｅｒｅｓultthatPrandWsformulaholdsgoodforthemeanwind

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strongwindgroup（windspeedat6meterslevel≧5.8m/sec)．Ａshegot

unreasonablyhighvalueofz｡＝１０cmforthelightwindgroup，ｈｅｓｔｏｐｐｅｄｔｈｅ IslandRangeofVsQmots） 充 9 ３ 〃 4 ０ 〃 3 ０ 〃 ２ １ 〃 ７１５１一 一Ⅷ州咽一 ２掛叫Ⅲ一 ８×１０−４ １ ０ 〃 1 ０ 〃 1 ０ 〃 ８０２９ １１１ ●●●●●●●● ●●●●●●●◆ ●●●●●●●● ３９１３ １１ Ｗａｋｅ SanJuan Johnson ５３７１ １１２ 、貼的妬 ０３６１ １１１２ １：１﹃１で上 ﹄０４貢ＯＰＯ ″″″″ ４１４７ １１１

6８ Ｍｅｍ・Ｆａｃ・Ｆｉｓｈ，ＫａｇｏｓｈｉｍａＵｎｉｖ，ｖｏｌ、４ furtherstudy，regardingtheobservationaldatawerenotavailableforsteady state・Forthestrongwindgroup，hefoundthatthewindprofileabovelOOcm obeysPrandWsformulawithz｡＝0.6ｃｍｂｕｔｂｅｌｏｗｔｈｉｓｌｅｖｅｌｉｔＯｂｅｙｓｖｏｎ Ｖ

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ｗｈｅｒｅｊノiskinematicviscosityofair． ThisfactwasalsoidentifiedbyhimfromtheanalysisofShoulejkinﾉsdata overtheBlackSeaandMontgomeryﾉsoverBuzzardsBay・ JO Ifweallowtheassumptionthatthｅｓｔａｔｅｏｆｔｌ]ＬｅＵｐｐｅｒｐａｒｔｏｆｓｋｉｎｌａｙｅｒ ｗｈｉｃｈｏｂｅysPrandtlﾉsformulaindicatesrealconditionｓｏｖｅｒｔｈｅｓｅａ，ｗｅｓｈａｌｌ ｂｅａｂｌｅｔｏｆｉｎｄｔｈｅvalueｏｆ応fromthecharacteroftheupperpartonlywith‐ outpayinganyattentiontothatofthelowestlayer・Ｔｈｕｓｗｅｈａｖｅに＝33×10-4 ｗｉｔｈｚ｡＝4ｃｍｆｒｏｍｔｈｅｍｅａｎｏｆＷｉｉｓｔﾉｓｄａｔａａｎｄ応＝20×10-4ｗｉｔｈｚ｡＝0.6cm fromthestrongwindgroup･Inthecalculation，ｗｅｃｈｏｏｓｅｚａ＝３０metersin ordertocomparethesewitｈＴａylorﾉsresultsofSalisburyP1ane・Ｔｈｅｓｅｖａｌｕｅｓ ｋｅｅｐｔｈｅｓａｍｅｏｒｄｅｒｏｆにａｓｉｎｔｈｅｃａｓｅｏｖｅｒｌａｎｄ，accordinglyweareobliged toconcludethatにisindependentofsurfacestatesb Butwemustrememberthattheseobservationsweremadeovertheshore waters，notoverthemid-ocean・Ｔｈｅassumption，ｔｈａｔｔｈｅｓtateoftheupper partovertheshorewatersisequivalenttotheconditiｏｎｏｖｅｒｔｈｅｏｐｅｎｓｅａ， isdoubtfuLInotherwords，wemustrecognizethattheupperpartismuch modifiedbythelandcondition，ｗｈｉｌｅｔｈｅｌｏｗｅＳｔｌａｙｅｒｉｓｆｒｅｅｆｒｏｍｔheland disturbance・Thus，ｉｔｍａｙｂｅｉｎｆｅｒｒｅｄｔｈａｔｗｈｅｎｔｈｅｏｂｓｅrvationsaremade overmid-oceanthewindprofilewhichobeysvonKarm加ﾉsformula，existing

inthelowestlayerovertheshorewaters，ｍａｙｂｅｅｘｔｅｎｄｅｄｔｏｔｈｅｕｐｐｅｒｐａｒｔ

ｏｆｔheskinlayer・ AsimilarsituationoverlandwasfoundinMildnerﾉspilotballoonobser‐ vationsinLeipzig・FromtheseObservationsLettau('0)deducedで｡‐valueｏｆ５．３１ dynes/cm2･Ｂｙｕｓｉｎｇｔｈｉｓｖａｌｕｅｗｅｇｅｔパー69×10-4,andconnectingthisvalue withtheskinlayer，ｗｅｏｂｔａｉｎｚ｡＝31.4ｃｍ･However，theobservationswere madeatthefieldwiththezO-valueofabout0.5ｃｍ・Thiscontradictionmaybe explaineｄｂｙｔｈｅｆａｃｔｔｈａｔｔｈｅａｉｒｒｅａｃｈｉｎｇｔｈｅｆｉｅｌｄｈａｄｊｕｓｔｂｅforepassed overthecity・ Fromthisreason，ｉｔｍａｙｂｅｓｕｐｐｏｓｅｄｔｈａｔｖｏｎＫａｒｍａｎﾉsformulaoverthe smoothsurfacewiｌｌｈｏｌｄｎｏｔｏｎｌｙｗｉｔｈｉｎｔｈｅｌｏｗｅｓｔｌａyerbutthroughoutthe skinlayerovertheactualsea・Ifweallowthissupposition，weshallhavethe l l

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7.6×１０−４ 6９ Wiist'ｓｄａｔａ（BalticSea） Ｔａｋａｈａｓｈｉ：Ｓｕｒｆａｃｅｒｅｓｉｓｔａｎｃｅｉｎｆｌｏｗｏｖｅｒｔｈｅｏｃｅａｎ Ｍｅａｎ ４．Summary Adeterminationofthecoefficientoftheskinfriction（だ）ｏｖｅｒｔｈｅｓｅａｉｓ ａｔｔｅｍｐｔｅｄｉｎｔｈｉｓｃｒｉticalnote・TheassumptionthatthecoefficienｔハＥｉｓｉｎｄｅ‐ pendentofsurfacestatesisdiscussed，ａｎｄｉｔｉｓｉｌｌｕｓｔｒａｔｅｄｂｙａｎｅｘａｍｐｌｅｔhat thisassumptionleadstoaresultcontradictorywiththeobservedfact・Ｐ.Ａ・ Sheppardandothersノdeterminationsofノｒｆｒｏmpilotballoonobservationsare reviewed，ａｎｄｉｔｉｓｎｏｔｉｃｅｄｔｈａｔｔｈｅｏｒｄｅｒｏｆｔｈeObtainedvalueofだ＝１０×１０−４ ｉｓreliable；ａｎｄｂｙｔｈｅｗａｙｔｈｅｖａｌｕｅｉｓａｂｏｕｔｏｎｅ−forthofthatoverland・ Rossbyrstreatmentforthedeterminationofにｆｒｏｍthevelocityprofilein theskinlayerisdiscussedinthelatterpartofthispaper・NoticingRosSby's resultsthatintheupperportionoftheskinlayerthewindprofileobeys PrandtlﾉsformulawhileinthelowerportionｉｔｏｂｅｙｓｖｏｎＫ６ｒｍ加ﾉsformulafor thesmoothsurface，thewriterofthispapersupposesthattheconditionofthe isnotexemptfromanymodification・Atpresent，wehavetoopoorobservation‐ almaterialstoexaminethesetheoreticalinconsistency・Leavingthisquestion Table2 Montgomery'ｓｄａｔａ（BuzzardsBay） 7.1．〃 ８ ． ３ 〃 ７ ． ７ 〃 ８ ． ２ 〃 ７ ． ７ 〃 陀 Series Ｖ 〔 ｍ / s e c ） ’ １ ５ １ ０ １ ５ ２ ０ ３ ０ ４ ０ Sept。 104だ ９ ． ２ ７ ． ４ ６ ． ８ ６ ． ５ ６ ． ３ ６ ． ０ ５ ． ８ 20th 22nd 23rd 24th unsettled，wecalculatethLevaluesofにｆｏｒdifferentV-valuesfromthisequa‐ tionwiththeresultslistedinTablｅ２．Inadditiontothese，thevaluesthus obtainedfromtheactualdatatreatedbyRossbyarefixeｄｉｎＴａｂｌｅ３･The orderofthesevaluescoincidesｗｉｔｈｔｈｅｖａｌｕｅｌＯ×１０−４indicatedinthepre‐ cedingsection・Inconseqllence，ｉｔｉｓｐｒｏｖｅｄｔｈａｔｔｈｅｖａｌｕｅｏｆ左isconsiderably lowerovertheseathanoverland． Table３ 7.8×１０−４ Materials Shoulejkin'sdataalackSea）

１２

８ ． ０ 〃 ７ ． ７ 〃 Inean Series

●● ﹃ロ’一︽函一垂︼ 7０ ●●● ヘベニ︾○如一一声畦二︾ Ｍｅｍ・ＦＦ１ｃ・Ｆｉｓｈ・ＫａｇｏｓｈｉｍａＵｎｉｖ・vol、４， upperportionoftheskinlayer，shownbytheavailabledataobserveｄａｔｎｅａｒ ｃｏａｓｔ，maybemuchmodifiedbytheneighbouringlandconditionwithoutrepre‐ sentingthetrueconditionovertheOpensea，whiletheconditionofthelower portionindicatesthetrueconditionovertheopensea・Ｉｎｔｈｉｓｖｉｅｗｐｏint,reject‐ ｉｎｇｔｈｅｔｏｏｈｉｇｈｖａｌｕｅｓｏｆだ（２０‐３３×10-4）obtainedfromtheupperprofiles oftheskinlayer，ａｎｄａｓｓｕｍｉｎｇｔｈａｔｖｏｎＫａｒｍａｎﾉｓｆｏｒｍｕｌａｉｓａｖａｉｌａｂｌｅｕｐ ｔｏｔｈｅｔｏｐｏftheskinlayer，thewriterfixesthevalue泥＝８×10-4,whichis comparablewiththevalueobtainedfromthepilotballoonobservationsover theopensea･ Acknowledgement………Thisauthorwishestoexpresshisheａｒｔｙｔｈａｎｋｓｔｏ Ｄｒ.Ｔ･Namekawa，ProfessorofKyotoUniversity,、forhisencouragementand helpfuladvicethroughoutthecourseofthiswork． Ｒｅｆｅｒｅｎｃｅｓ ノ C､Ｍ,GuldbergandH・Mohn,1876：EtudessurlesMouvementsdeL'atInosphdre． Ｇ､1.Ｔａｙｌｏｒ，１９１６：ＳｋｉｎＦｒｉｃｔｉｏｎｏｎｔｈｅＥａｒｔｈ'ｓＳｕｒｆ旬ｃｅｓ，Proc，Ｒｏｙ・ＳＯＣ．Ｌon．Ａ， vol、９２． ，.Brunt，１９３９：ＰｈｙｓｉｃａｌandDynamicalMeteorology． Ｗ､Ｎ・Ｓｈａｗ，１９３１：ManualofMeteorology，ＣａｍｂｒｉｄｇｅUniv・Ｐｒｅｓｓ． Ｒ､Ｃ､Sutcliffe，１９３６：SurfaceResistanceinAtmosphricFlow，Quart．Ｊ・Roy・Met・ ＳＯＣ.，vol、６２． Ｐ.Ａ・Sheppard,Ｈ・Charnock，ａｎｄＪ.Ｒ､Ｄ･Francis，１９５２：ObservationsoftheWesterlies oveｒｔｈｅＳｅａ，Quart.』・Roy、Met・ＳＯＣ.，vol、７８，ｎｏ、338． Ｐ.Ａ･Ｓｈｅｐｐ可ｒｄａｎｄＭ．Ｈ･Ｏｍａｒ，１９５２：ＴｈｅＷｉｎｄＳｔｒｅｓｓｏｖｅｒｔｈｅＯｃｅａｎｆｒｏｍＯｂｓｅ‐ ｒｖａｔｉｏｎｓｉｎｔｈｅＴｒａｄｅｓ，Ｉｂｉｄ． Ｃ､Ｇ・ＲｏｓｓｂｙａｎｄＲ.Ｂ・Ｍｏｎｔｇｏｍｅｒｙ，１９３５：TheLayerofFrictionalInfluenceiｎＷｉｎｄ ａｎｄＯｃｅａｎＣｕｒｒｅｎｔｓ，ＰａｐｅｒｓｉｎＰｈｙｓ･Ｏｃｅａｎｏｇ･ａｎｄＭｅｔ.，vol、３，ｎｏ､３． Ｃ､Ｇ・Ｒｏｓｓｂｙ，１９３６：ＯｎｔｈｅＦｒｉｃｔｉｏｎａｌＦｏｒｃｅｂｅｔｗｅｅｎＡｉｒａｎｄＷａｔｅｒａｎｄｏｎｔｈｅＯＣＣ‐ ｕｒｒｅｎｃｅｏｆａＬａｍｉｎａｒＢｏｕｎｄａｒｙＬａｙｅｒｎｅｘｔｔｏｔｈｅＳｕｒｆｎｃｅｏｆｔｈｅＳｅａ，Ｐａｐｅｒｓｉｎ Ｐｈｙｓ･Ｏｃｅａｎｏｇ･ａｎｄＭｅｔ.，vol､４，ｎｏ､３． Ｈ･Letｔａｕ，１９５０：ＡＲｅ−ｅｘａｍｉｎａｔｉｏｎｏｆｔｈｅ〃LeipzigWindProfile〃consideringSome RelationsbetweeｎＷｉｎｄａｎｄＴｕｒｂｕｌｅｎｃｅｉｎｔｈｅＦｒｉｃｔｉｏｎａｌＬａｙｅｒ，Tellｕｓ，vol、２，ｎｏ､２． 9 ． 1０． 6． ７． 8 ．